Art, Bruce, and Charlie were running for sheriff. In the election, a total of 15,424 votes were cast. Art received 1006 more than Bruce and 1213 more than Charlie. How many votes did each candidate receive?
| Art: | x + 1006 and y + 1213 |
| Bruce: | x votes |
| Charlie: | y votes |
| x + 1006 + x + y = 15424 | → | 2x + y = 14418 |
| x + 1006 = y + 1213 | → | x – y = 207 |
| 3x = 14625 → x = 4875 (Bruce) | ||
| x + 1006 = 5881 (Art) | ||
| 15424 – (4875 + 5881) = 4668 (Charlie) |
Can this problem be done without using formal algebra?